Pak.j.stat.oper.res. Vol.18 No.1 2022 pp 85-97 DOI: http://dx.doi.org/10.18187/pjsor.v18i1.3904 Bayesian analysis of an M |M |1|∞ queueing model Naveen K. Bansal 1* , V.S. Vaidyanathan 2 , P. Chandrasekhar 3 * Corresponding author 1. Department of Mathematical and Statistical Sciences, Marquette University, Wisconsin, USA, naveen.bansal@marquette.edu 2. Department of Statistics, Pondicherry University, Puducherry, India, vaidya.stats@gmail.com 3. Department of Statistics, Loyola College, Chennai, India, drchandrasekharin@yahoo.co.in Abstract In this paper, by considering an M |M |1|∞ queueing model, Bayesian estimation of traffic intensity and measures of system performance are worked out under the squared error loss function (SELF) based on the observed data on independent interarrival and service times. Further, minimum posterior risk associated with Bayes estimators of traffic intensity and system performance measures are obtained under SELF. Numerical illustration of the performance of the estimates is given through simulation study. It is shown that Bayes estimators perform better than the maximum likelihood estimators under the influence of prior informations. Key Words: Bayes estimator, exceedance probability, M |M |1|∞ queue, queue length, queue system size, squared error loss function, traffic intensity. Mathematical Subject Classification: Primary 60K25; Secondary 90B22. 1. Introduction Queueing models are often used in the design and analysis of telecommunication systems, traffic systems, service systems and so on. Since the arrival time and service time of entities in the queue are stochastic, it will be of interest to carry out inferential procedures to study and analyze the behaviour of the parameters of the queueing models by assuming suitable probability distributions. This can be done either through the fre- quentist or Bayesian approach. In case where the probability distribution of either or both of the arrival and service times are not known, non-parametric inferential procedures can be employed to analyze the queueing model; see for example Schweer and Wichelhaus (2015). In this paper, we take a parametric approach by assuming exponential distributions for arrival and service times. A detailed survey on different inferential procedures and its applications to various queueing models can be found in Asanjarani et al. (2021). Among many queueing models available in the literature, M |M |1|∞ model has received more attention primarily due to less model complexities. This model assumes only one service station and does not put a cap on the queue size. The main purpose of this article is to apply certain statistical inference procedures for an M |M |1|∞ queueing model with Poisson input and exponential service times from a Bayesian perspective. It is often the case that information is available on the parameters of the interarrival or service time distribution from prior experiments or from prior analysis of the interarrival or service time data. Bayesian approach provides the methodology by incorporating prior information to the current data. Bayesian analysis of an M|M|1|∞ queueing model 85